Zero Crossing Of Second Directional Derivative Edge Operator

We use the facet model to accomplish step edge detection. The essence of the facet model is that any analysis made on the basis of the pixel values in some neighborhood has its final authoritative interpretation relative to the underlying grey tone intensity surface of which the neighborhood pixel values are observed noisy samples. Pixels which are part of regions have simple grey tone intensity surfaces over their areas. Pixels which have an edge in them have complex grey tone intensity surfaces over their areas. Specifically, an edge moves through a pixel if and only if there is some point in the pixel's area having a zero crossing of the second directional derivative taken in the direction of a non-zero gradient at the pixel's center. To determine whether or not a pixel should be marked as a step edge pixel, its underlying grey tone intensity surface must be estimated on the basis of the pixels in its neighborhood. For this, we use a functional form consisting of a linear combination of the tensor products of discrete orthogonal polynomials of up to degree three. The appropriate directional derivatives are easily computed from this kind of a function. Upon comparing the performance of this zero crossing of second directional derivative operator with Prewitt gradient operator and the Marrâ€"Hildreth zero crossing of Laplacian operator, we find that it is the best performer and is followed by the Prewitt gradient operator. The Marr-Hildreth zero-crossing of Laplacian operator performs the worst.